On Feb 13, 9:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote: <snip>
> You cannot discern that two potentially infinity sequences are equal. > When will you understand that such a result requires completeness?
Nope
Two potentially infinite sequences x and y are equal iff for every natural number n, the nth FIS of x is equal to the nth FIS of y No concept of completeness is needed or used.
E.G,
we can use induction to show
x={1,1+2,1+2+3,...,1+2+...+n,...}
is equal to
y={(1)(2)/2,(2)(3)/2,(3)(4)/2,...,n(n+1)/2,...}
Consider the list of potentially infinite sequence L1= 1000... 11000... 111000... ...
L2= 111... 11000... 111000... ...
The diagonals are both d=111...
It makes perfect sense to say that there is no line in L1 that is equal to d but there is a line in L2 that is equal to d
